Adding a texture map to a beveled curve or path
Yes, you can. Just simply toggle the Use UV for mapping option in Properties Editor > Object Data Tab > Texture space panel.



For BI render


In order to use UV coordinate, you have to convert the curve object into a mesh object to store UV (AltC > 2). Just besure to have that optio toggled, which will automatically generate a neat UV (named Orco by default). and set Texture coornidate to UV:





If you don't want to convert the curve object into a mesh, for regular use, you have a nice option, by using Generated coodinate instead for texture:




For Cycles Render:


After toggling Use UV for mapping option, you can immidiately see the automatic Orco UV in 3D View, Cycles will by default use UV coordinate for both curve and mesh: